Acta Mathematica

The tempered spectrum of a real spherical space

Friedrich Knop, Bernhard Krötz, and Henrik Schlichtkrull

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Let $G/H$ be a unimodular real spherical space which is either absolutely spherical, i.e. the real form of a complex spherical space, or of wave-front type. It is shown that every tempered representation for $G/H$ embeds into a twisted discrete series for a boundary degeneration of $G/H$. If $G/H$ is of wave-front type it follows that the tempered representation is parabolically induced by a twisted discrete series representation for a real spherical space formed by a Levi subgroup.


The second author was supported by ERC Advanced Investigators Grant HARG 268105.

Article information

Acta Math., Volume 218, Number 2 (2017), 319-383.

Received: 30 September 2015
Revised: 12 August 2016
First available in Project Euclid: 31 January 2018

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Knop, Friedrich; Krötz, Bernhard; Schlichtkrull, Henrik. The tempered spectrum of a real spherical space. Acta Math. 218 (2017), no. 2, 319--383. doi:10.4310/ACTA.2017.v218.n2.a3.

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